Problem: Simplify the following expression: $x = \dfrac{5a^2 + 10a - 75}{a - 3} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ x =\dfrac{5(a^2 + 2a - 15)}{a - 3} $ Then we factor the remaining polynomial: $a^2 + {2}a {-15} $ ${-3} + {5} = {2}$ ${-3} \times {5} = {-15}$ $ (a {-3}) (a + {5}) $ This gives us a factored expression: $\dfrac{5(a {-3}) (a + {5})}{a - 3}$ We can divide the numerator and denominator by $(a + 3)$ on condition that $a \neq 3$ Therefore $x = 5(a + 5); a \neq 3$